Cross-Impact

Nonparametric Estimation of Self- and Cross-Impact ArXiv ID: 2510.06879 “View on arXiv” Authors: Natascha Hey, Eyal Neuman, Sturmius Tuschmann Abstract We introduce an offline nonparametric estimator for concave multi-asset propagator models based on a dataset of correlated price trajectories and metaorders. Compared to parametric models, our framework avoids parameter explosion in the multi-asset case and yields confidence bounds for the estimator. We implement the estimator using both proprietary metaorder data from Capital Fund Management (CFM) and publicly available S&P order flow data, where we augment the former dataset using a metaorder proxy. In particular, we provide unbiased evidence that self-impact is concave and exhibits a shifted power-law decay, and show that the metaorder proxy stabilizes the calibration. Moreover, we find that introducing cross-impact provides a significant gain in explanatory power, with concave specifications outperforming linear ones, suggesting that the square-root law extends to cross-impact. We also measure asymmetric cross-impact between assets driven by relative liquidity differences. Finally, we demonstrate that a shape-constrained projection of the nonparametric kernel not only ensures interpretability but also slightly outperforms established parametric models in terms of predictive accuracy. ...

Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework ArXiv ID: 2503.05594 “View on arXiv” Authors: Unknown Abstract We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic terminal and running targets. Initially, we formulate the optimal trade execution task as a stochastic control problem with a finite-variation control process that acts as an integrator both in the state dynamics and in the cost functional. We then extend this problem continuously to a stochastic control problem with progressively measurable controls. By identifying this extended problem as equivalent to a certain linear-quadratic stochastic control problem, we can use established results in linear-quadratic stochastic control to solve the extended problem. This work generalizes [“Ackermann, Kruse, Urusov; FinancStoch'24”] from the single-asset setting to the multi-asset case. In particular, we reveal cross-hedging effects, showing that it can be optimal to trade in an asset despite having no initial position. Moreover, as a subsetting we discuss a multi-asset variant of the model in [“Obizhaeva, Wang; JFinancMark'13”]. ...

How does liquidity shape the yield curve? ArXiv ID: 2409.12282 “View on arXiv” Authors: Unknown Abstract The phenomenology of the forward rate curve (FRC) can be accurately understood by the fluctuations of a stiff elastic string (Le Coz and Bouchaud, 2024). By relating the exogenous shocks driving such fluctuations to the surprises in the order flows, we elevate the model from purely describing price variations to a microstructural model that incorporates the joint dynamics of prices and order flows, accounting for both impact and cross-impact effects. Remarkably, this framework allows for at least the same explanatory power as existing cross-impact models, while using significantly fewer parameters. In addition, our model generates liquidity-dependent correlations between the forward rate of one tenor and the order flow of another, consistent with recent empirical findings. We show that the model also account for the non-martingale behavior of prices at short timescales. ...

Optimal Portfolio Choice with Cross-Impact Propagators ArXiv ID: 2403.10273 “View on arXiv” Authors: Unknown Abstract We consider a class of optimal portfolio choice problems in continuous time where the agent’s transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate this problem as the maximization of a revenue-risk functional, where the agent also exploits available information on a progressively measurable price predicting signal. We solve the maximization problem explicitly in terms of operator resolvents, by reducing the corresponding first order condition to a coupled system of stochastic Fredholm equations of the second kind and deriving its solution. We then give sufficient conditions on the matrix-valued propagator so that the model does not permit price manipulation. We also provide an implementation of the solutions to the optimal portfolio choice problem and to the associated optimal execution problem. Our solutions yield financial insights on the influence of cross-impact on the optimal strategies and its interplay with alpha decays. ...

When is cross impact relevant? ArXiv ID: 2305.16915 “View on arXiv” Authors: Unknown Abstract Trading pressure from one asset can move the price of another, a phenomenon referred to as cross impact. Using tick-by-tick data spanning 5 years for 500 assets listed in the United States, we identify the features that make cross-impact relevant to explain the variance of price returns. We show that price formation occurs endogenously within highly liquid assets. Then, trades in these assets influence the prices of less liquid correlated products, with an impact velocity constrained by their minimum trading frequency. We investigate the implications of such a multidimensional price formation mechanism on interest rate markets. We find that the 10-year bond future serves as the primary liquidity reservoir, influencing the prices of cash bonds and futures contracts within the interest rate curve. Such behaviour challenges the validity of the theory in Financial Economics that regards long-term rates as agents anticipations of future short term rates. ...